Glossary

Divided differences

The recursive coefficients that build the interpolating polynomial in Newton form.

Definition

They are defined by $f[x_i]=f(x_i)$ and $f[x_i,\dots,x_{i+k}]=\frac{f[x_{i+1},\dots,x_{i+k}]-f[x_i,\dots,x_{i+k-1}]}{x_{i+k}-x_i}$ . They are the coefficients of the Newton form and sit in a triangular table that is easy to extend.

How it is used

Their big practical advantage: adding a new node only costs one more diagonal of the table, without rebuilding the whole polynomial.